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Zamolodchikov-Faddeev algebras for Yangian doubles at level 1

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Abstract

The representation theory of centrally extended Yangian doubles is investigated. The intertwining operators are constructed for infinite dimensional representations of\(\widehat{DY(\mathfrak{s}\mathfrak{l}_2 )}\), which are deformed analogs of the highest weight representations of the affine algebra\(\widehat{\mathfrak{s}\mathfrak{l}}_2 \) at level 1. We give bosonized expressions for the intertwining operators and verify that they generate an algebra isomorphic to the Zamolodchikov-Faddeev algebra for the SU(2)-invariant Thirring model. From them, we compose L-operators by Miki’s method and verify that they coincide with L-operators constructed from the universal R-matrix. The matrix elements of the product of these operators are calculated explicitly and are shown to satisfy the quantum (deformed) Knizhnik-Zamolodchikov equation associated with the universal R-matrix for\(\widehat{DY(\mathfrak{s}\mathfrak{l}_2 )}\).

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Authors and Affiliations

  1. Institute of Theoretical and Experimental Physics, Bol. Cheremushkinskaya 25, 117259, Moscow

    D. R. Lebedev

  2. Joint Institute of Nuclear Research, 141980, Dubna, Moscow region

    S. Z. Pakuliak & S. M. Khoroshkin

Authors
  1. D. R. Lebedev
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  2. S. Z. Pakuliak
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  3. S. M. Khoroshkin
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Additional information

This paper was written at the request of the Editorial Board.

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 25–45. January, 1997.

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Lebedev, D.R., Pakuliak, S.Z. & Khoroshkin, S.M. Zamolodchikov-Faddeev algebras for Yangian doubles at level 1. Theor Math Phys 110, 18–34 (1997). https://doi.org/10.1007/BF02630366

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  • DOI: https://doi.org/10.1007/BF02630366

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